Math & Computer Science Colloquium Series

Dr. Chris Godsil of the University of Waterloo presents Continuous Quantum Walks on Graphs as part of the Math & Computer Science Colloquium Series.

If A is the adjacency matrix of a graph X , then the matrix exponential U (t) = exp(itA) determines what physicists term a continuous quantum walk. They ask questions such as: for which graphs are the vertices a and b and a t such that |U (t)a,b | = 1? The basic problem is to relate the physical properties of the system with properties of the underlying graphs, and to study this we make use of results from the theory of graph spectra, number theory, ergodic theory.